1. Field of the Invention
This invention is related to the field of wellbore logging instruments. More specifically, the present invention is related to logging instruments which measure the bulk density of earth formations. The instrument of the invention includes a plurality of sensors used for compensating the bulk density measurements for the presence of "mudcake" on the wall of a wellbore wherein the mudcake has indeterminate bulk density and thickness.
2. Description of the Related Art
Well logging instruments are used to evaluate earth formations penetrated by wellbores for the presence of useful materials such as petroleum. Well logging instruments are typically lowered into the wellbore at one end of an armored electrical cable which conducts power to the instruments and returns measurement signals to the earth's surface for recording and observation. The instruments include sensors which measure various properties of the earth formations.
Measurements of the bulk density of the earth formations are particularly useful. Bulk density measurements are used for, among other things, determining the fractional volume of pore space in the earth formations in which fluids such as oil and gas may be present; determining the mineral composition of the earth formation and for determining the weight, or overburden force, of the earth formation at any particular depth in the wellbore.
Well logging instruments known in the art for determining bulk density of the earth formation are typically derived from an instrument disclosed in U.S. Pat. No. 3,321,625 issued to Wahl. The instrument in the Wahl '625 patent includes a source of gamma rays having a predetermined energy magnitude. The source is typically a steady-state, radioisotopic chemical source such as cesium-137. The tool in the Wahl '625 patent includes two gamma-ray photon detectors positioned at spaced apart locations from the source. The source and detectors are typically disposed in a high-density (typically metallic tungsten) "pad" or "skid" mounted to one side of the tool, which restricts the gamma ray output of the source to be principally in the direction of the earth formation, and controls the entry of gamma rays into the detectors to be primarily from the direction of the earth formation. The skid is typically placed into firm contact with the wall of the wellbore by means of a powered, extensible arm directed from the opposite side of the tool on which the skid is located.
Gamma rays from the source can interact with electrons orbiting atoms in the materials forming the earth formation. Each interaction can cause a gamma ray to lose some of its energy and be deflected from its original direction of travel. The source is typically selected so that the original energy magnitude of the gamma rays facilitates this type of interaction, known as Compton scattering. The rate at which gamma rays lose energy and are deflected from their original directions is related to both the electron density of the earth formation (the number of electrons per unit volume of the formation) and the distance between the source and the detector. Some gamma rays can survive the Compton scattering process and return to the detectors. The counting rate at any one of the detectors resulting from Compton-scattered gamma rays can be described by the relationship: EQU I=I.sub.o e.sup.-.mu.x ( 1)
where I represents the counting rate at a detector having a spacing x from the source, I.sub.o represents the count rate of a detector at zero spacing from the source, and .mu. represents an "absorption" coefficient which is related to the electron density of the earth formation in contact with the skid and axially interposed between the source and particular detector. For most materials from which earth formations are typically composed, electron density is directly related to bulk density, so the measurements of detector count rates can be directly scaled into measurements of bulk density of the formation by using the relationship in equation (1).
As is disclosed in the Wahl '625 patent, the skid typically does not perfectly contact the wall of the wellbore. Wellbores are typically drilled with a fluid suspension, called "drilling mud" in which solid components of the suspension "plate out" to form an impermeable barrier across permeable earth formations which have lower fluid pressure than the hydrostatic pressure of the fluid column of drilling mud in the wellbore. The impermeable barrier, called "mud filtrate" or "mud cake", can in some instances exceed one inch in thickness. The mud filtrate would therefore typically be interposed between the skid and the wall of the wellbore. The instrument in the Wahl '625 patent provides a form of compensation for the interposition of mud filtrate between the wellbore wall and the skid by using two detectors at different axially spaced apart locations from the source. The detector positioned at the greater axial distance from the source (the "far-spacing" detector) will be responsive to gamma rays which have interacted with electrons at a greater radial distance from the wall of the wellbore than those reaching the other detector (the "near-spacing" detector). As is disclosed in the Wahl '625 patent, an empirical relationship is devised which relates the count rates at both detectors to a bulk density of the earth formation and a "correction" for various thicknesses and densities of mud cake. The empirical relationship is typically devised by inserting the tool into media of known bulk densities and including simulated "mud cake", typically rubber or plastic sleeves, of known densities and thicknesses in between the skid and the particular density medium. The count rates at the two detectors are recorded for each of the known conditions. Non-zero values of "correction" are indicated when count rates at both detectors deviate from count rates indicative of perfect contact with the wall of the wellbore, which in devising the empirical relationship are found by inserting the tool in the media with no "artificial mud cake" interposed between the skid and any of the media.
A drawback to the bulk density instruments known in the art derived from the Wahl '625 patent is that they generally require that the wall of the wellbore be reasonably smooth, and that the mud filtrate typically not exceed about one inch in thickness.
Several improvements to the apparatus disclosed in the Wahl '625 patent have been devised which seek to overcome the limitations of wellbore smoothness and maximum mudcake thickness suffered by the apparatus disclosed therein. For example U.S. Pat. No. 5,390,115 issued to Case et al. discloses a density instrument having three detectors at axially spaced apart locations from the source. Case et al. claim to be able to correct for mudcakes having thicknesses in excess of one inch. While Case et al. state that the measurements made by their apparatus are substantially independent of the density of the formation and the density of the mudcake, the error bounds and the conditions under which the apparatus disclosed will function correctly are not recited by Case et al.
U.S. Pat. No. 5,530,243 issued to Mathis discloses a density instrument having an array of sensors at axially spaced apart locations from the source to compensate for tool tilt and roughness of the wall of the wellbore. The apparatus disclosed in Mathis '243 does provide improved performance over the apparatus disclosed in Wahl '625, but the apparatus in Mathis '243 requires the use of a neural network to determine thickness of the mudcake and correction to the density readings therefrom. Training neural networks can be difficult and expensive.
The invention is intended to provide the improved performance of a density instrument having an array of detectors without the need to train a neural network.